The Pentagon ran into more trouble from Republicans on Capitol Hill yesterday, as House GOP leaders drafted a budget alternative that would cut President Reagan's defense spending request by $8 billion more than a Senate-approved budget that the White House has criticized as inadequate.

The latest setback for the Pentagon came as Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) urged the president, during a meeting with congressional leaders at the White House, to support the Senate plan in order to fend off further losses on defense.

Domenici also told Reagan and Secretary of Defense Caspar W. Weinberger that they had to give Congress "real evidence" of any possible damage to national defense from congressional spending plans if they hoped to recoup the losses.

"To cry wolf isn't enough," Domenici said after the meeting. "You have to give real documentation."

Despite Domenici's warnings about the risk of further losses in the absence of White House support for the Senate plan, administration officials reportedly continued to criticize it. And Senate sources said the House Republican leaders' plan could make it all the more difficult to get a House-Senate budget compromise that approximates even the Senate proposal for defense.

"It certainly isn't helpful," Domenici said.

With this apparently in mind, the House GOP leaders were said by aides to be undecided whether to present their alternative for a vote when the House begins debate today on its version of a fiscal 1987 budget. A decision will be made after the plan is submitted for discussion at a morning caucus of House Republicans, the aides said.

In their draft of the budget, House GOP leaders proposed to set defense spending authority for next year at $293 billion, or $27 billion less than Reagan requested and $8 billion less than the Senate proposed in the budget it approved last month.

In a plan approved last week by the House Budget Committee, House Democrats proposed $285 billion in spending authority for defense, with $3 billion held in reserve until the Pentagon accounts for all its current spending.

Unlike the Senate budget and the plan approved by the House Budget Committee, the House GOP leaders' proposal does not include tax increases opposed by Reagan. Like the other two plans, it meets the $144 billion deficit target set for next year by the new Gramm-Rudman-Hollings budget-control law.

A House Republican leadership aide described the $293 billion defense allocation embraced by GOP leaders as "what they felt was a consensus position on defense" among House Republicans consulted during the drafting process.

White House spokesman Larry Speakes indicated that during the meeting with congressional leaders, Reagan was especially critical of the House Democrats' defense spending proposal, although the president continued to voice reservations about the Senate plan.

"I have serious reservations about some individual aspects of the Senate budget resolution," Speakes quoted Reagan as saying. "But the House budget resolution is totally unacceptable. It represents the classic Democratic budgetary solution -- slash defense, raise taxes and protect unneeded domestic programs."

House Budget Committee Chairman William H. Gray III (D-Pa.), reacting to earlier White House criticism of the House plan, took issue with distinctions between the House and Senate plans, saying that there is a "very small difference" between the two, especially in actual outlays for defense over a three-year period. "Of course," he added, "the White House is screaming that the Russians are coming up the Potomac."

At the White House meeting, Senate Republicans were reportedly irritated when Office of Management and Budget Director James C. Miller III characterized the House Democrats' plan as representing the budget priorities of former Democratic presidential nominees George S. McGovern and Walter F. Mondale, and suggested that the Senate plan was not all that different.

Senate Majority Leader Robert J. Dole (R-Kan.) "didn't appreciate that comment," said one source. Dole has been championing the White House cause on defense, insisting that the Senate stand by its $301 billion defense figure in negotiations with the House on a final budget compromise.

Meanwhile, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said he will support the Democrats' budget plan on the House floor, even if Republicans do not endorse the tax increases. But O'Neill continued to insist on bipartisan support for actual tax increases.